a) \(A\left(-3;0\right);B\left(1;0\right)\)
\(\overrightarrow{AB}=\left(1+3;0\right)=\left(4;0\right)\)
\(3\overrightarrow{MA}-2\overrightarrow{MB}=\left(1;0\right)\)
\(\Leftrightarrow3\overrightarrow{MA}-2\overrightarrow{AB}-2\overrightarrow{AM}=\left(1;0\right)\)
\(\Leftrightarrow3\overrightarrow{MA}+2\overrightarrow{MA}-2\overrightarrow{AB}=\left(1;0\right)\)
\(\Leftrightarrow5\overrightarrow{MA}-2\overrightarrow{AB}=\left(1;0\right)\)
\(\Leftrightarrow\left\{{}\begin{matrix}5\left(-3-x_M\right)-2.4=1\\5\left(1-y_M\right)-2.0=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}-3-x_M=\dfrac{9}{5}\\1-y_M=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x_M=-3-\dfrac{9}{5}=-\dfrac{24}{9}\\y_M=1\end{matrix}\right.\) \(\Rightarrow M\left(-\dfrac{24}{9};1\right)\)
a: vecto MA=(-3-x;-y)
vecto MB=(1-x;-y)
3*vecto MA-2*vecto MB=(1;0)
=>3(-3-x)-2(1-x)=1 và 3*(-y)-2*(-y)=0
=>-9-3x-2+2x=1 và y=0
=>-11-x=1 và y=0
=>x=-12 và y=0
b: vecto NA=(-3-x;-y)
vecto NB=(1-x;y)
vecto AB=(4;0)
vecto NA+3*vecto NB=vecto AB
=>-3-x+3(1-x)=4 và -y+3y=0
=>-3-x+3-3x=4 và y=0
=>-4x=4 và y=0
=>x=-1 và y=0
b) \(\overrightarrow{NA}+3\overrightarrow{NB}=\overrightarrow{AB}\)
\(\Leftrightarrow\overrightarrow{NA}+3\overrightarrow{AB}-3\overrightarrow{AN}=\overrightarrow{AB}\)
\(\Leftrightarrow\overrightarrow{AN}+3\overrightarrow{AN}=3\overrightarrow{AB}-\overrightarrow{AB}\)
\(\Leftrightarrow4\overrightarrow{AN}=2\overrightarrow{AB}\)
\(\Leftrightarrow2\overrightarrow{AN}=\overrightarrow{AB}\)
\(\Leftrightarrow\left\{{}\begin{matrix}2\left(x_N+3\right)=4\\2\left(y_N-0\right)=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x_N+3=2\\y_N=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x_N=-1\\y_N=0\end{matrix}\right.\) \(\Rightarrow N\left(-1;0\right)\)
